Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1

• Published in: Finite fields and their applications Vol. 78
• Main Authors: Kim, Boran, Han, Nayoung, Lee, Yoonjin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2022
• Subjects: Additive code; Chain ring; Gray map; Optimal code; Self-orthogonal code; secondary; Gray map; Additive code; Optimal code; Chain ring; primary; Self-orthogonal code
• ISSN: 1071-5797; 1090-2465
• DOI: 10.1016/j.ffa.2021.101972

We find a building-up type construction method for self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉. Our construction produces self-orthogonal codes over Z4 with increased lengths and free ranks from given self-orthogonal codes over Z4 with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over Z4 with generator matrix subject to certain conditions can be obtained from our construction. Employing our construction method, we obtain at least 125 new self-orthogonal codes over Z4 up to equivalence; among them, there are 35 self-orthogonal codes which are distance-optimal. Furthermore, we have eight self-orthogonal codes, which are distance-optimal among all linear codes over Z4 with the same type. As a method, we use additive codes over the finite ring Z4[u]/〈u2+1〉 with generator matrices G satisfying GGT=O, and we use a new Gray map from Z4[u]/〈u2+1〉 to Z43 as well.